Jaime Barrera - Academia.edu (original) (raw)

Papers by Jaime Barrera

We analyze a two-dimensional discrete-time SIS model with a non-constant total population. Our go... more We analyze a two-dimensional discrete-time SIS model with a non-constant total population. Our goal is to determine the interaction between the total population, the susceptible class and the infective class, and the implications this may have for the disease dynamics. Utilizing a constant recruitment rate in the susceptible class, it is possible to assume the existence of an asymptotic limiting equation which enables us to reduce the system of two-equations into a single, dynamically equivalent equation. In this case, we are able to demonstrate the global stability of the disease-free and the endemic equilibria when the basic reproductive number (R 0) is less than one and greater than one, respectively. When we consider a non-constant recruitment rate, the total population bifurcates as we vary the birth rate and the death rate. Using computer simulations, we observe different behavior among the infective class and the total population, and possibly, the ocurrence of a strange attractor.

August 1999 We analyze a two-dimensional discrete-time SIS model with a non-constant total popula... more August 1999 We analyze a two-dimensional discrete-time SIS model with a non-constant total population. Our goal is to determine the interaction between the total population, the susceptible class and the infective class, and the implications this may have for the disease dynamics. Utilizing a constant recruitment rate in the susceptible class, it is possible to assume the existence of an asymptotic limiting equation which enables us to reduce the system of twoequations into a single, dynamically equivalent equation. In this case, we are able to demonstrate the global stability of the disease-free and the endemic equilibria when the basic reproductive number (Ro) is less than one and greater than one, respectively. When we consider a nonconstant recruitment rate, the total population bifurcates as we vary the birth rate and the death rate. Using computer simulations, we observe different behavior among the infective class and the total population, and possibly, the ocurrence of a strange attractor.

Revista de Matemática: Teoría y Aplicaciones, 2012

We analyze a two-dimensional discrete-time SIS model with a nonconstant total population. Our goa... more We analyze a two-dimensional discrete-time SIS model with a nonconstant total population. Our goal is to determine the interaction between the total population, the susceptible class and the infective class, and the implications this may have for the disease dynamics. Utilizing a constant recruitment rate in the susceptible class, it is possible to assume the existence of an asymptotic limiting equation which enables us to reduce the system of two-equations into a single, dynamically equivalent equation. In this case, we are able to demonstrate the global stability of the disease-free and the endemic equilibria when the basic reproductive number (Ro) is less than one and greater than one, respectively. When we consider a non-constant recruitment rate, the total population bifurcates as we vary the birth rate and the death rate. Using computer simulations, we observe different behavior among the infective class and the total population, and possibly, the ocurrence of a strange attractor.

We study the interactions between normal and abnormal cell populations as they occur in a tumorou... more We study the interactions between normal and abnormal cell populations as they occur in a tumorous growth. The purpose of our research is determine whether the spatial arrangement of abnormal cells in a tissue is a significant factor governing the spread of the tumor. To this end, we model how normal and abnormal cells compete for nutrients using a deterministic model and a spatial stochastic model. We vary nutrient competition rates as well as drug treatment effects for the two cell populations. The deterministic model indicates how the populations interact without consideration of spatial arrangement, while the stochastic model includes this factor. Our results show that different spatial arrangements of cells may cause significant differences in the growth dynamics of the cells even if the initial population sizes are kept constant. We have found that the spatial model reveals some growth dynamics that the deterministic model overlooks. Therefore it is of interest to obtain more realistic spatial models. For this, we ; , need to focus research on the most distinctive factor of the spatial model: how normal and malignant cells on the boundary of a tumor compete for nutrients.

Narcotics ruins people's lives in the United States everyday. The United States government not on... more Narcotics ruins people's lives in the United States everyday. The United States government not only imposes stiff sentences on drug dealers but also spends billions of dollars a year developing programs to try to reduce the high intensity of drug distribution in cities across the United States. Unfortunately there is still a high number of narcotics being distributed within the United States. We use a stochastic model to study the trends of drug dealer populations set into motion as a result of fixing a set of incarceration times for drug dealers. We then project these trends and calculate costs associated with jailing drug dealers and the associated active drug dealer distributions. Specific questions that we are address include: Do a fixed set of incarceration times set trends in drug dealer populations? For a fixed set of incarceration times, how much does it cost to jail drug dealers 5 years? For 10 years? What do these costs buy? Are there less drug dealers as a result of these policies?

and especially Johnny Guzman and Anael Verdugo. Uncountably many thanks go to my family, especial... more and especially Johnny Guzman and Anael Verdugo. Uncountably many thanks go to my family, especially my brother George, for giving their unconditional support, and love, and for living without me for so long while I finished this endeavor. I thank my wife, Wichittra Kung Khammee, for unconditional love, support and inspiration.

We analyze a two-dimensional discrete-time SIS model with a non-constant total population. Our go... more We analyze a two-dimensional discrete-time SIS model with a non-constant total population. Our goal is to determine the interaction between the total population, the susceptible class and the infective class, and the implications this may have for the disease dynamics. Utilizing a constant recruitment rate in the susceptible class, it is possible to assume the existence of an asymptotic limiting equation which enables us to reduce the system of two-equations into a single, dynamically equivalent equation. In this case, we are able to demonstrate the global stability of the disease-free and the endemic equilibria when the basic reproductive number (R 0) is less than one and greater than one, respectively. When we consider a non-constant recruitment rate, the total population bifurcates as we vary the birth rate and the death rate. Using computer simulations, we observe different behavior among the infective class and the total population, and possibly, the ocurrence of a strange attractor.

August 1999 We analyze a two-dimensional discrete-time SIS model with a non-constant total popula... more August 1999 We analyze a two-dimensional discrete-time SIS model with a non-constant total population. Our goal is to determine the interaction between the total population, the susceptible class and the infective class, and the implications this may have for the disease dynamics. Utilizing a constant recruitment rate in the susceptible class, it is possible to assume the existence of an asymptotic limiting equation which enables us to reduce the system of twoequations into a single, dynamically equivalent equation. In this case, we are able to demonstrate the global stability of the disease-free and the endemic equilibria when the basic reproductive number (Ro) is less than one and greater than one, respectively. When we consider a nonconstant recruitment rate, the total population bifurcates as we vary the birth rate and the death rate. Using computer simulations, we observe different behavior among the infective class and the total population, and possibly, the ocurrence of a strange attractor.

Revista de Matemática: Teoría y Aplicaciones, 2012

We analyze a two-dimensional discrete-time SIS model with a nonconstant total population. Our goa... more We analyze a two-dimensional discrete-time SIS model with a nonconstant total population. Our goal is to determine the interaction between the total population, the susceptible class and the infective class, and the implications this may have for the disease dynamics. Utilizing a constant recruitment rate in the susceptible class, it is possible to assume the existence of an asymptotic limiting equation which enables us to reduce the system of two-equations into a single, dynamically equivalent equation. In this case, we are able to demonstrate the global stability of the disease-free and the endemic equilibria when the basic reproductive number (Ro) is less than one and greater than one, respectively. When we consider a non-constant recruitment rate, the total population bifurcates as we vary the birth rate and the death rate. Using computer simulations, we observe different behavior among the infective class and the total population, and possibly, the ocurrence of a strange attractor.

We study the interactions between normal and abnormal cell populations as they occur in a tumorou... more We study the interactions between normal and abnormal cell populations as they occur in a tumorous growth. The purpose of our research is determine whether the spatial arrangement of abnormal cells in a tissue is a significant factor governing the spread of the tumor. To this end, we model how normal and abnormal cells compete for nutrients using a deterministic model and a spatial stochastic model. We vary nutrient competition rates as well as drug treatment effects for the two cell populations. The deterministic model indicates how the populations interact without consideration of spatial arrangement, while the stochastic model includes this factor. Our results show that different spatial arrangements of cells may cause significant differences in the growth dynamics of the cells even if the initial population sizes are kept constant. We have found that the spatial model reveals some growth dynamics that the deterministic model overlooks. Therefore it is of interest to obtain more realistic spatial models. For this, we ; , need to focus research on the most distinctive factor of the spatial model: how normal and malignant cells on the boundary of a tumor compete for nutrients.

Narcotics ruins people's lives in the United States everyday. The United States government not on... more Narcotics ruins people's lives in the United States everyday. The United States government not only imposes stiff sentences on drug dealers but also spends billions of dollars a year developing programs to try to reduce the high intensity of drug distribution in cities across the United States. Unfortunately there is still a high number of narcotics being distributed within the United States. We use a stochastic model to study the trends of drug dealer populations set into motion as a result of fixing a set of incarceration times for drug dealers. We then project these trends and calculate costs associated with jailing drug dealers and the associated active drug dealer distributions. Specific questions that we are address include: Do a fixed set of incarceration times set trends in drug dealer populations? For a fixed set of incarceration times, how much does it cost to jail drug dealers 5 years? For 10 years? What do these costs buy? Are there less drug dealers as a result of these policies?

and especially Johnny Guzman and Anael Verdugo. Uncountably many thanks go to my family, especial... more and especially Johnny Guzman and Anael Verdugo. Uncountably many thanks go to my family, especially my brother George, for giving their unconditional support, and love, and for living without me for so long while I finished this endeavor. I thank my wife, Wichittra Kung Khammee, for unconditional love, support and inspiration.